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A new proof for part of the noncrossed product theorem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1145-1151 Cet article a éte moissonné depuis la source Math-Net.Ru

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The first examples of noncrossed product division algebras were given by Amitsur in 1972. His method is based on two basic steps: (1) If the universal division algebra $U(k,n)$ is a $G$-crossed product then every division algebra of degree $n$ over $k$ should be a $G$-crossed product; (2) There are two division algebras over $k$ whose maximal subfields do not have a common Galois group. In this note, we give a short proof for the second step in the case where $\operatorname{char} k\nmid n$ and $p^3|n$.
Keywords: division algebra, crossed product
Mots-clés : valuation. 
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M. Motiee. A new proof for part of the noncrossed product theorem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1145-1151. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a11/

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